Question: Heidi grew her hair out for many years. Her hair was $1\dfrac{1}{3}$ of a meter long. She donated her hair by cutting off $\dfrac{5}{6}$ of a meter. How long is Heidi's hair now?
Answer: To find the length of Heidi's hair now, we need to subtract. $1\frac{1}{3}$ $\frac{5}{6}$ length of Heidi's hair amount of hair cut length of hair now ${1\dfrac{1}{3}} - {\dfrac{5}{6}} = \text{ length of hair now}}$ Our denominators need to be the same so we can subtract. What is the least common multiple for the denominators $3$ and $6$ ? The least common multiple of $3$ and $6$ is ${6}$. ${\dfrac13}={\dfrac{1}{3}} \times {\dfrac{2}{2}} = {\dfrac{2}{6}}$ Now, let's subtract. $\begin{aligned} &{1} &{\dfrac{2}{6}}\\\\ -&{0}&{\dfrac{5}{6}}\\ \hline\\ \end{aligned}$ We need to regroup ${1}{\dfrac{2}{6}}$ so that the fractional part is greater than ${\dfrac{5}{6}}$. $\begin{aligned} {1} {\dfrac{2}{6}} &={\dfrac66} + {\dfrac{2}{6}}\\\\ &={\dfrac{8}{6}} \end{aligned}$ Now that our fractions have the same denominator and our first fraction is greater than our second fraction, we can subtract. $\begin{aligned} &\overset{{0}}{\cancel{{1}} }&{\dfrac{\overset{{8}}{\cancel{2}}}{6}}\\\\ -&{0}&{\dfrac{5}{6}}\\ \hline\\ &{0}&{\dfrac{3}{6}} \end{aligned}$ The length of Heidi's hair now is $\dfrac{3}{6}$ of a meter. This answer can also be written as $\dfrac{1}{2}$ of a meter.